Chris Froome of Team Sky competed in the recent criterium in Belgium, but not in last week's London-Surrey Classic. Photograph: David Stockman/AFP/Getty Images

Chris Froome missed a trick this week. It was an important one, something that could have brought him the recognition he may feel is missing in his adopted country following his victory in the Tour de France.

After a rider has won the Tour, the next couple of weeks follow a long-established script. He spends them in Belgium, Holland and northern France, riding in criteriums – evening races around town centre circuits, sponsored by local businesses – that bring him a fair chunk of cash, perhaps up to €50,000 per race. It's a tradition dating back to the days when cyclists were not paid the sort of salary that Froome now commands: just north of £2m a year under his new deal. And it's a tradition worth preserving, because the crowds at those races represent regions with a deep-rooted passion for bike racing.

After that, a Tour winner's time is his own for a while. In all probability he will be fancying a holiday, which is the option Froome took. Had he chosen to keep his Lycra on for one more day, however, he could have ridden in Sunday's London-Surrey Classic, the 140-mile race for professionals that followed the Prudential RideLondon 100-mile sportive for around 16,000 amateur riders.

In terms of an addition to his trophy cabinet, it would have been next to meaningless – although the win certainly meant a lot to Arnaud Démare, the gifted 21-year-old Frenchman who sprinted up the Mall with his arms raised, taking a measure of revenge for all those Mark Cavendish victories on the Champs-Elysées. But from the perspective of Froome's standing in Britain, the value of his participation would have been immeasurable.

He is a modest, rather private and quietly eloquent man who has worked hard for everything he has achieved. The fact that he was born far away, in a country where bike racing was not part of the general cultural curriculum, makes his success all the more remarkable. Perhaps, too, that unlikely background makes it easier to explain.

His rise to prominence reminds me of the footballer Owen Hargreaves, another outsider who had to fight for the right to succeed in his chosen sport. Born in Canada to British parents, raised in a land where football barely registered, Hargreaves left home as a teenager to forge his own destiny, first in Germany and then in England. In both countries he survived early scepticism to make a powerful mark. He won European Cup winner's medals with Bayern Munich and Manchester United and was virtually the only England player to emerge with credit from the 2006 World Cup before persistent knee problems truncated his career.

With England, too, he had to win over the fans, who took a while to overcome an instinctive desire to jeer a stranger before recognising that he, not Wayne Rooney or Frank Lampard or John Terry, was the closest thing the team had to a pivotal figure. A core of mental strength hardened by the experience of trusting himself to cope with the unknown was surely what helped him become the only England player to score from the penalty spot in the catastrophic quarter-final shootout against Portugal in Gelsenkirchen.

Similarly, Dave Brailsford's decision to invite Froome to join his new Team Sky squad in 2010 was not immediately hailed as a stroke of genius. Few others had spotted the young Kenyan-born rider's potential during his three seasons in Europe, hidden away among the Konica-Minolta and Barloworld teams. A mysterious illness impeded his progress in his first two seasons with Sky, and until a proper diagnosis of the parasitical infection was made he stayed well under the radar. So there was much surprise during last year's Tour when he showed himself capable of outpacing Bradley Wiggins, the team leader and eventual winner, on the more demanding mountain stages. Given the fervent British desire for a Wiggins victory, Froome's momentary willingness to ignore the script made him an object of suspicion.

Froome's father is British, and he has always had a British passport, but he has never lived in the United Kingdom. His first home in Europe was near Lake Como and on joining Sky he moved further south to the team's Italian base in Tuscany. Two years ago he settled in Monaco with his girlfriend – now fiancee – Michelle Cound, who was born in Wales but brought up in South Africa. He is happy to declare his allegiance to Britain, but the small Kenyan emblem on the frame of his racing bike is a clear symbol of his fundamental affection for Africa – including South Africa, where he went to secondary school and university.

So there is no reason, beyond paternity and the fact that his team's HQ is in Manchester, why he should harbour special feelings for Britain. Yet God Save the Queen was played as he stood on the podium in Paris, and he has been acclaimed as Britain's second winner of the greatest of all bike races. Recent precedent suggests that there should be something for him in the next honours list.

All of which makes it seem a shame that he was not in London last weekend. The sight of the maillot jaune hammering through the centres of Kingston, Weybridge, Dorking, Esher and Wimbledon, powering up Leith Hill and Box Hill and finishing in front of Buckingham Palace would have added to the exhilaration so clearly experienced both by the participants in the earlier ride and the spectators lining the course during a memorable day for cycling not just in the south-east but in Britain as a whole.

Given his split loyalties, Froome has negotiated the last few months adroitly, reaffirming allegiances while saying nothing that would upset either his fellow Kenyans or his adoptive compatriots. But someone close to him should have remembered the sort of tumultuous response Wiggins and Mark Cavendish received when they competed in last year's Tour of Britain, giving home crowds a sight of their champions, and recognised that his appearance would have done a great deal to close whatever emotional distance exists between the rider and his new public. Just for turning up and demonstrating the aura of the jersey, he would have been bathed in admiration.

Neither Wiggins nor Cavendish rode on Sunday. The former was in Poland as part of the programme to get him fit for next month's world championships, while the latter fulfilled a commitment to ride in the Tour of Denmark. For Froome, however, there were no such competing obligations. In the extraordinary saga of British cycling's surge to world domination, his decision to stay away represents a rare misstep.